Wikipedia has a fairly-good article on the nature of Familiars, at least as far as classic magical familiars go. Familiars basically are companions and aides of their "masters" - often linked mentally/spiritually/magically to their masters in some fashion, providing certain benefits to both parties.
Familiars serve their master's bidding somewhat akin to a pet, albeit a "pet with benefits" you might say. Classic familiars who are not initially sapient (like ordinary cats, spiders, frogs, owls, etc.) often become so, and may gain supernatural abilities like resistance to injury, supernatural luck (which they often share with their masters), or the ability to share thoughts and ideas, and maybe even skills, tricks and spells, over the link between them.
I'd say the humans cohabitating with Cypress would be the closest example in Felarya to a classic familiar. They're linked to her through the dryad-link, they technically serve her (although she's magnanimous about it and doesn't ask for much beyond food) and there's benefits to the linked state - she can protect and communicate with them, they relay information back to her and provide her with food.
As far as Léa goes, I don't think she'd qualify as a familiar. She's just a friend of Crisis who happens to not care for her own kind anymore. Perfectly reasonable IMO - I'd rather care more about one person who genuinely loved me than a whole species who didn't, even if they were my own. As for Gunther... he's just a greedy opportunist.